{"abstract":"Inverse tangent drops odd symmetry.","category":"Floating-point arithmetic","checks":8,"contract":"Evaluate inverse hyperbolic tangent on [-1,1], with signed infinite endpoints and a domain marker outside. Finite results are rendered to eleven significant decimal digits; modeled domain violations and arithmetic errors are explicit strings.","contract_signature":"x","evaluation_group":"s3-float-atanh-stable","failed_approach":"The attempted local correction return render(-result) still violates the explicit regression fixtures.","family":"s3-floating_point_arithmetic-atanh-stable-odd-sign","id":"FA-16211","implementations":{"attempt":{"sha256":"ba90fa47c7e0061265323cc4c4c448f60f14ae4118dcdda0a200df22d70f14b7","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\ndef render(x):\n    if math.isnan(x): return 'nan'\n    if math.isinf(x): return '-infinity' if x<0 else '+infinity'\n    return format(x,'.11g')\n\nN = 1\nobservations = []\ndef solve(x):\n    try:\n        if abs(x)>1: return 'domain'\n        if x==1: return '+infinity'\n        if x==-1: return '-infinity'\n        if x==0: return render(x)\n        a=abs(x)\n        result=0.5*math.log1p(2*a/(1-a))\n        return render(-result)\n    except (ValueError, OverflowError, ZeroDivisionError, TypeError):\n        return \"arithmetic-error\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('tiny positive', solve(N*2.0**-60), render(N*2.0**-60))\ncheck('tiny negative', solve(-N*2.0**-60), render(-N*2.0**-60))\ncheck('normal', solve(0.125*N), render(math.atanh(0.125*N)))\ncheck('negative normal', solve(-0.125*N), render(math.atanh(-0.125*N)))\ncheck('positive endpoint', solve(1.0), \"+infinity\")\ncheck('negative endpoint', solve(-1.0), \"-infinity\")\ncheck('invalid', solve(1.0+N), \"domain\")\ncheck('negative zero', solve(-0.0), \"-0\")\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"1776cf8f37d38c9d0449e2d00f1135058674d645019b5de48f09f9b46898404e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\ndef render(x):\n    if math.isnan(x): return 'nan'\n    if math.isinf(x): return '-infinity' if x<0 else '+infinity'\n    return format(x,'.11g')\n\nN = 1\nobservations = []\ndef solve(x):\n    try:\n        if abs(x)>1: return 'domain'\n        if x==1: return '+infinity'\n        if x==-1: return '-infinity'\n        if x==0: return render(x)\n        a=abs(x)\n        result=0.5*math.log1p(2*a/(1-a))\n        return render(result)\n    except (ValueError, OverflowError, ZeroDivisionError, TypeError):\n        return \"arithmetic-error\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('tiny positive', solve(N*2.0**-60), render(N*2.0**-60))\ncheck('tiny negative', solve(-N*2.0**-60), render(-N*2.0**-60))\ncheck('normal', solve(0.125*N), render(math.atanh(0.125*N)))\ncheck('negative normal', solve(-0.125*N), render(math.atanh(-0.125*N)))\ncheck('positive endpoint', solve(1.0), \"+infinity\")\ncheck('negative endpoint', solve(-1.0), \"-infinity\")\ncheck('invalid', solve(1.0+N), \"domain\")\ncheck('negative zero', solve(-0.0), \"-0\")\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Controlled binary64 or explicitly stipulated miniature format; no hardware exception flags or platform floating environment are modeled. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-floating_point_arithmetic-atanh-stable-odd-sign","generated_at":"2026-09-29T14:39:34.357219+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"An offline floating representation model isolates a reproducible arithmetic fault.","root_cause":"Inverse tangent drops odd symmetry. The faulty expression is return render(result).","sha256":"b4e9cb577a5939710632745120ce1f7f250ba25b23498e676ba288364899c468","title":"Inverse tangent drops odd symmetry · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":40.999,"exit_code":1,"observations":[{"actual":"-8.6736173799e-19","check":"tiny positive","expected":"8.6736173799e-19","passed":false},{"actual":"-8.6736173799e-19","check":"tiny negative","expected":"-8.6736173799e-19","passed":true},{"actual":"-0.12565721414","check":"normal","expected":"0.12565721414","passed":false},{"actual":"-0.12565721414","check":"negative normal","expected":"-0.12565721414","passed":true},{"actual":"+infinity","check":"positive endpoint","expected":"+infinity","passed":true},{"actual":"-infinity","check":"negative endpoint","expected":"-infinity","passed":true},{"actual":"domain","check":"invalid","expected":"domain","passed":true},{"actual":"-0","check":"negative zero","expected":"-0","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"tiny positive\", \"actual\": \"-8.6736173799e-19\", \"expected\": \"8.6736173799e-19\", \"passed\": false}, {\"check\": \"tiny negative\", \"actual\": \"-8.6736173799e-19\", \"expected\": \"-8.6736173799e-19\", \"passed\": true}, {\"check\": \"normal\", \"actual\": \"-0.12565721414\", \"expected\": \"0.12565721414\", \"passed\": false}, {\"check\": \"negative normal\", \"actual\": \"-0.12565721414\", \"expected\": \"-0.12565721414\", \"passed\": true}, {\"check\": \"positive endpoint\", \"actual\": \"+infinity\", \"expected\": \"+infinity\", \"passed\": true}, {\"check\": \"negative endpoint\", \"actual\": \"-infinity\", \"expected\": \"-infinity\", \"passed\": true}, {\"check\": \"invalid\", \"actual\": \"domain\", \"expected\": \"domain\", \"passed\": true}, {\"check\": \"negative zero\", \"actual\": \"-0\", \"expected\": \"-0\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.023,"exit_code":1,"observations":[{"actual":"8.6736173799e-19","check":"tiny positive","expected":"8.6736173799e-19","passed":true},{"actual":"8.6736173799e-19","check":"tiny negative","expected":"-8.6736173799e-19","passed":false},{"actual":"0.12565721414","check":"normal","expected":"0.12565721414","passed":true},{"actual":"0.12565721414","check":"negative normal","expected":"-0.12565721414","passed":false},{"actual":"+infinity","check":"positive endpoint","expected":"+infinity","passed":true},{"actual":"-infinity","check":"negative endpoint","expected":"-infinity","passed":true},{"actual":"domain","check":"invalid","expected":"domain","passed":true},{"actual":"-0","check":"negative zero","expected":"-0","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"tiny positive\", \"actual\": \"8.6736173799e-19\", \"expected\": \"8.6736173799e-19\", \"passed\": true}, {\"check\": \"tiny negative\", \"actual\": \"8.6736173799e-19\", \"expected\": \"-8.6736173799e-19\", \"passed\": false}, {\"check\": \"normal\", \"actual\": \"0.12565721414\", \"expected\": \"0.12565721414\", \"passed\": true}, {\"check\": \"negative normal\", \"actual\": \"0.12565721414\", \"expected\": \"-0.12565721414\", \"passed\": false}, {\"check\": \"positive endpoint\", \"actual\": \"+infinity\", \"expected\": \"+infinity\", \"passed\": true}, {\"check\": \"negative endpoint\", \"actual\": \"-infinity\", \"expected\": \"-infinity\", \"passed\": true}, {\"check\": \"invalid\", \"actual\": \"domain\", \"expected\": \"domain\", \"passed\": true}, {\"check\": \"negative zero\", \"actual\": \"-0\", \"expected\": \"-0\", \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}